基于Oseen代的有限差异方法,用于解决二维Navier-Stokes方程
1College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China.
Entropy (Basel, Switzerland)
|May 27, 2023
概括
这项研究引入了一种用于解决复杂流体流量问题的新型数值方法. 带有Oseen代的辐射基础函数有限差异方法为纳维埃-斯托克斯方程提供了简化和准确的方法.
科学领域:
- 计算流体动力学的流体动力学.
- 数字分析 数字分析
- 流体力学 流体力学 流体力学
背景情况:
- 纳维埃-斯托克斯方程是流体动力学的基础,但由于它们的非线性性质,很难在数值上解决.
- 现有的数值方法通常涉及复杂的矩阵运算,增加计算成本.
- 需要有效和准确的方法来模拟不可压缩的流体流.
研究的目的:
- 开发和验证一种新的数值方法来解决二维稳定不可压缩的纳维埃-斯托克斯方程.
- 通过在非线性代过程中最大限度地减少矩阵重新计算来提高计算效率.
- 为了实现流体流量问题的高精度数值解决方案.
主要方法:
- 空间运算符的分离,使用射线基础函数和多项式基础函数的有限差异方法.
- 应用Oseen代方案来处理纳维尔-斯托克斯方程中的非线性项.
- 构建一个离散方案,结合半径基函数有限差和Oseen代.
主要成果:
- 拟议的方法通过避免在每个非线性代中完全重组矩阵来简化计算过程.
- 获得了高精度的数值解决方案,证明了方法的有效性.
- 数字示例证实了光线基函数有限差法与Oseen代的收性和准确性.
结论:
- 射线基函数有限差方法,与Oseen代集成,为解决二维稳定不可压缩的纳维埃-斯托克斯方程提供了一种高效和准确的技术.
- 与传统方法相比,这种方法在计算简单性方面具有显著的优势.
- 经验证的有效性表明,在计算流体动力学研究和工程中具有广泛的适用性.
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